Inclusion Criteria:

          -  Participants must have either of the following:

               -  Relapsed/refractory leukemia in 2nd or greater relapse or who have failed at
                  least one re-induction attempt after relapse or for refractory disease. Patients
                  must meet the WHO classification with ≥ 5% blasts in the bone marrow or must have
                  definitive extramedullary disease (e.g. chloromas, skin lesions). Patients may
                  have asymptomatic CNS 1 or CNS 2 disease, but not CNS 3 or symptomatic CNS
                  disease.

        OR

          -  Relapsed/refractory non-CNS solid tumor that has not responded or has relapsed and for
             which no standard treatment is available. Patients may not have primary CNS tumors or
             CNS metastases. Lymphoma patients are permitted. Patients do not need to have
             measurable disease.

               -  Age 6 months - 29.99 years at enrollment

               -  Life expectancy >/= 3 months

               -  Lansky or Karnofsky >/= 50

               -  Prior therapy

          -  Participant must have fully recovered from the acute toxic effects of all prior
             chemotherapy, immunotherapy, radiotherapy, or surgery prior to study entry.

          -  Myelosuppressive therapy - At least 14 days must have elapsed since the administration
             of previous therapy. Six weeks must have elapsed from the administration of
             nitrosoureas or mitomycin C. For participants with ALL on maintenance therapy, they
             may be eligible if 7 days have elapsed and they are recovered from the toxic effects
             of the chemotherapy. This restriction does not include intrathecal chemotherapy, which
             is permitted. Hydroxyurea is permitted but must be discontinued >/= 24 hours prior to
             start of protocol therapy.

          -  Biologic agents - At least 14 days must have elapsed since the completion of therapy
             with a biologic agent such as a monoclonal antibody. Seven days must have elapsed
             since the last dose of retinoids

          -  Radiation therapy - At least 14 days must have elapsed for local XRT. At least 90 days
             must have elapsed if prior radiation to >/= 50% of the pelvis, the spine, or other
             substantial bone marrow radiation including TBI.

          -  Hematopoietic growth factors - At least 7 days must have elapsed since the last dose
             of G-CSF or GM-CSF. At least 14 days must have elapsed since last dose of
             pegfilgrastim (Neulasta).

               -  Participants must be >/= 3 months from hematopoietic stem cell transplant, must
                  not have active GVHD, and must be off all immunosuppression

        Laboratory

          -  Organ function:

               -  Either a serum creatinine </= ULN for age, of calculated or measured GFR >/= 70
                  mL/min/1.73 m2

               -  Total bilirubin </= 1.5 x ULN for age, direct bilirubin </= ULN for age

               -  AST and ALT </= 3 x ULN for age unless elevation can be clearly attributed to
                  liver leukemia or metastases

               -  ECHO shortening fraction >/= 27%

               -  Pulse oximetry measurement >/= 95% saturation without supplemental oxygen

          -  Bone marrow function

               -  Hgb >/= 10 g/dL - can be transfused

               -  Plts >/= 75,000 - cannot be transfused (must be >/= 7 days from last plt
                  transfusion)

               -  ANC >/= 750 - cannot be transfused (must be >/= 72 hours from last neutrophil
                  infusion) However, the ply and ANC requirements can be waived if low counts
                  through to be secondary to leukemia or tumor bone marrow infiltration

        Ethical/Other

          -  Reproductive function

               -  Female participants of childbearing potential must have a negative serum
                  pregnancy test confirmed within 7 days prior to enrollment

               -  Female participants with infants must agree not to breastfeed their infants while
                  on the study

               -  Male and female participants of child-bearing potential must agree to use an
                  effective method of contraception approved by the investigator during the study
                  and for a minimum of 3 months after study treatment

          -  Written informed consent

        Exclusion Criteria:

          -  Prior treatment with carfilzomib

          -  Known allergy to Captisol (a cyclodextrin derivative used to solubilize carfilzomib)

          -  Down syndrome

          -  Fanconi Anemia or other underlying bone marrow failure syndrome

          -  Pregnant or lactating females

          -  Known history of Hepatitis B or C or HIV

          -  Participant with any significant concurrent illness

          -  Participant with uncontrolled systemic fungal, bacterial, viral or other infection
             with ongoing signs/symptoms despite appropriate treatment

          -  Participant with illness, psychiatric disorder or social issue that could compromise
             participant safety or compliance with the protocol treatment or procedures, interfere
             with the consent, study participation, follow-up, or interpretation of study results